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An ExpanderBased Approach to Geometric Optimization
 IN PROC. 9TH ANNU. ACM SYMPOS. COMPUT. GEOM
, 1993
"... We present a new approach to problems in geometric optimization that are traditionally solved using the parametric searching technique of Megiddo [34]. Our new approach ..."
Abstract

Cited by 40 (16 self)
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We present a new approach to problems in geometric optimization that are traditionally solved using the parametric searching technique of Megiddo [34]. Our new approach
3D Vertical Ray Shooting and 2D Point Enclosure, Range Searching, and Arc Shooting Amidst Convex Fat Objects
 COMPUT. GEOM. THEORY APPL
, 1995
"... We present a new data structure for a set of n convex simplyshaped fat objects in the plane, and use it to obtain efficient and rather simple solutions to several problems including (i) vertical ray shooting  preprocess a set K of n nonintersecting convex simplyshaped flat objects in 3space, ..."
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Cited by 23 (4 self)
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We present a new data structure for a set of n convex simplyshaped fat objects in the plane, and use it to obtain efficient and rather simple solutions to several problems including (i) vertical ray shooting  preprocess a set K of n nonintersecting convex simplyshaped flat objects in 3space, whose xyprojections are fat, for efficient vertical ray shooting queries, (ii) point enclosure  preprocess a set C of n convex simplyshaped fat objects in the plane, so that the k objects containing a query point p can be reported efficiently, (iii) boundedsize range searching  preprocess a set C of n convex fat polygons, so that the k objects intersecting a `nottoolarge' query polygon can be reported efficiently, and (iv) boundedsize segment shooting  preprocess a set C as in (iii), so that the first object (if exists) hit by a `nottoolong' oriented query segment can be found efficiently. For the first three problems we construct data structures of size O(s (n) log 3 n)...
Biased Finger Trees and ThreeDimensional Layers of Maxima
, 1994
"... We present a method for maintaining biased search trees so as to support fast finger updates (i.e., updates in which one is given a pointer to the part of the tree being changed). We illustrate the power of such biased finger trees by showing how they can be used to derive an optimal O(n log n) algo ..."
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Cited by 10 (4 self)
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We present a method for maintaining biased search trees so as to support fast finger updates (i.e., updates in which one is given a pointer to the part of the tree being changed). We illustrate the power of such biased finger trees by showing how they can be used to derive an optimal O(n log n) algorithm for the 3dimensional layersofmaxima problem and also obtain an improved method for dynamic point location.
Algorithms for Performing Polygonal Map Overlay and Spatial Join on Massive Data Sets
 Advances in Spatial Databases6th International Symposium, SSD ’99, Hong Kong
, 1999
"... . We consider the problem of performing polygonal map overlay and the refinement step of spatial overlay joins. Weshowhowto adapt algorithms from computational geometry to solve these problems for massive data sets. A performance study with artificial and realworld data sets helps to identify t ..."
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Cited by 5 (0 self)
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. We consider the problem of performing polygonal map overlay and the refinement step of spatial overlay joins. Weshowhowto adapt algorithms from computational geometry to solve these problems for massive data sets. A performance study with artificial and realworld data sets helps to identify the algorithm that should be used for given input data. 1 Introduction During the last couple of years Spatial and GeoInformation Systems (GIS) have been used in various application areas, likeenvironmental monitoring and planning, rural and urban planning, and ecological research. Users of suchsystems frequently need to combine two sets of spatial objects based on a spatial relationship. In twodimensional vector based systems combining twomapsm 1 and m 2 consisting of polygonal objects by map overlay or spatial overlay join is an important operation. The spatial overlay join of m 1 and m 2 produces a set of pairs of objects (o 1 #o 2 ) where o 1 2 m 1 #o 2 2 m 2 , and o 1 and o 2...
Message Compression for High Performance
 Proc. 7th. SIAM Conference on Parallel Processing, San Franscisco
, 1995
"... this paper. ..."